Energy levels are discrete, not continuous. For example, electrons orbit neutron and protons with discrete values of energy. Yet it has been understood for a some time that the transition from one electron orbital energy level to another is not instantaneous (Bohr and Heisenberg thought it was instantaneous, Schrödinger and Einstein disagreed, that dispute was resolved decades ago in favor of the latter). How is it possible to have discontinuous energy levels and simultaneously have a continuous transition between different energy levels?
There is a one word answer: Superposition. We do not witness superposition as a phenomena in our daily lives, yet superposition is essential and ubiquitous. An electron can have a particular energy level, then be in a continuously changing superposition of two different energy levels until it completes its transition to the other energy level. Superposition enables a continuous transition between states whose values are restricted to jumps between discrete values.
It has recently been demonstrated experimentally that it is possible to detect when a transition between different energy levels is about to occur in advance and then to intervene quickly enough to prevent the transition from completing (see https://quantuminstitute.yale.edu/publications/quantum-theory-peels-away-mystery-measurement). The jump between energy levels is at least partly deterministic, with enough information it can be predicted in advance and reversed. But the information needed to predict the jump is available only for a short time in advance. Over a longer time frame the jump between energy levels remains unpredictable and can only be modeled stochastically (this is arguably because of a lack of information availability, not necessarily because of an underlying indeterminism).
With superposition our universe is a hybrid mix of discrete and continuous phenomena. Is our universe also a mix of supernatural and natural phenomena? Many people have thought so and most people continue to think so. But on closer examination naturalism alone appears to suffice. Our imaginations did not discover superposition, we discovered superposition from empirical evidence. We have no similar evidence that there is any unmet need for anything beyond the natural despite the many opportunities for supernaturalism to have been properly evidenced.